Question: Simplify the following expression: $x = \dfrac{60n^3 + 24n^2}{60n^3 - 66n^2}$ You can assume $n \neq 0$.
Answer: Find the greatest common factor of the numerator and denominator. The numerator can be factored: $60n^3 + 24n^2 = (2\cdot2\cdot3\cdot5 \cdot n \cdot n \cdot n) + (2\cdot2\cdot2\cdot3 \cdot n \cdot n)$ The denominator can be factored: $60n^3 - 66n^2 = (2\cdot2\cdot3\cdot5 \cdot n \cdot n \cdot n) - (2\cdot3\cdot11 \cdot n \cdot n)$ The greatest common factor of all the terms is $6n^2$ Factoring out $6n^2$ gives us: $x = \dfrac{(6n^2)(10n + 4)}{(6n^2)(10n - 11)}$ Dividing both the numerator and denominator by $6n^2$ gives: $x = \dfrac{10n + 4}{10n - 11}$